A wounded past
From the conversation, Zain concluded that Kun was a zombie that had yet to evolve. Although he did seem fast, it wasn't to the point where one believes it was super speed.
The fact was, Zain didn't know if Kun was even capable of evolving or levelling up like him, he needed more information, and perhaps this group of other zombies similar to him would be the place to find it.
Observing Kun, Zain noticed that he was a bit paranoid about things and wouldn't bother to explain why. He insisted on turning off all the lights and asked him not to stay as far away from the window as possible.
Although zombies didn't need sleep, resting appeared to decrease the energy depletion rate, and Kun refused to talk and put his finger on his own mouth every time Zain spoke, signalling him to remain silent. With all this, the latter had stopped there.